Harmony Among Men, Mastery of Math in the ‘Three Character Classic’

Yang Hui (Pascal’s) triangle, as depicted by Zhu Shijie in 1303, using counting rods. The Chinese mathematician Yang Hui discovered this triangular array 300 years before his French counterpart Blaise Pascal was born.

The Three Character Classic, or San Zi Jing, is the best known classic Chinese text for children. Written by Wang Yinlian (1223–1296) during the Song Dynasty, it has been memorized by generations of Chinese, both young and old. Until the 1800s, the Three Character Classic was the very first text that every child would study.

The text’s rhythmic, short, and simple three-character verses allowed for easy reading and memorization. This enabled children to learn common characters, grammar structures, lessons from Chinese history, and above all how to conduct oneself.

The Three Character Classic says:

Begin with filial piety and fraternal love,and then see and hear.Learn to count,and learn to read.

Units and tens,tens and hundreds,hundreds and thousands,thousands and tens of thousands.

The Three Forcesare Heaven, Earth and Man.The Three Luminariesare the sun, the moon and the stars.

The Three Bondsare the obligation between sovereign and subject,the love between father and child,the harmony between husband and wife.

Begin with filial piety and fraternal love, and then see and hear.

— Three Character Classic

After teaching young readers the fundamentals of being a good child and sibling, the Three Character Classic devotes a good amount of text to the basics of mathematics and numbers.

But it does more than teach kids how to solve “one plus one”. While teaching counting, the Three Character Classic associates each number with a fundamental piece of knowledge about nature, geography, society, and culture.

According to the ancient divination text I-Ching, there are three forces or “talents” in our environment – Heaven, Earth, and Man. The person who knows all three well is an all-rounded individual.

There are three sources of light that illuminate our skies – the sun, the moon and the stars. There are four seasons, and four directions – North, South, East and West.

The numbers serve as a useful memory aid, helping kids collate and remember lists like the five elements and the seven emotions in Chinese culture.

Numbers are such fundamental things that even young children know them by heart. But when did the Chinese develop numerals, and how much did they achieve in their numeration system and mathematics?

The Origins of Chinese Numerals

According to Chinese legend, the number one (一) was invented by Fu Xi, the first mythical emperor of China, over 5,000 years ago. The remaining numbers were created about 500 years later by Cangjie, the inventor of Chinese characters.

Shortly after, Li Shou, a historian for the Yellow Emperor, developed the decimal numeration system where ten tens are one hundred; ten hundreds are one thousand; and so on.

Legends aside, the earliest physical evidence of Chinese numerals dates back to the Shang Dynasty (14th century BC), over 3,000 years ago. Chinese numerals were found carved on tortoise shells and flat cattle bones – also known as oracle bones.

During that time, the Chinese were already using individual symbols for the numbers one through nine, indicating that the Chinese were among the first civilizations to use a decimal numeration system.

The decimal numeration system is the system most widely used by modern civilizations. This includes the numeration system we use today – the Hindu-Arabic system.

Chinese mathematicians were able to compute square and cube roots of numbers to several decimal places.

— Three Character Classic

Around 4th century BC, the Chinese also developed the world’s first decimal positional numeration system – counting rods – to make calculations easier.

This system proved extremely efficient, and Chinese mathematicians were able to compute square and cube roots of numbers to several decimal places. By 500 AD they had obtained the value for pi to 3.14159267, one thousand years ahead of their European counterparts. They were also the first to discover and prove “Pascal’s Triangle” – 300 years before Pascal was born!

Balancing the ‘Three Relationships’

The Three Bonds are the obligation between sovereign and subject, the love between father and child, the harmony between husband and wife.

— Three Character Classic

Among the “sets of three” that the Three Character Classic teaches are the Three Bonds or Three Relationships – the relationships between ruler and subject, between parent and child, and between couples.

These three relationships are the most important relationships among men and women, according to Confucian ideology. If these three relationships are handled well, one will enjoy peace and harmony. But if these relationships are handled poorly, one’s life will be in chaos.

One historic person who handled the three relationships well was Xu Yun, military general for the State of Wei during the Three Kingdoms Period. However, Xu Yun very nearly failed to achieve this, if not for his intelligent wife.

Xu Yun and Lady Ruan.

When he was a young man, Xu Yun was match-made to Lady Ruan, the daughter of Ruan Gong. But after the wedding ceremony, Xu Yun was shocked to see how plain and unattractive his new wife was under her wedding veil. He refused to enter the bridal chamber, and to the chagrin of his family, asked for a marriage annulment.

It took a fair amount of convincing by Xu’s family before Xu entered the bridal chamber. But upon seeing his bride, Xu could bear it no longer and turned to leave. Knowing that he would not return, his wife stopped him by pulling on his robes.

To embarrass his wife, Xu Yun said derisively, “Out of the four feminine virtues – feminine character, skills, speech, and appearance – how many do you possess?”

His wife replied, “What I lack is simply beauty. A scholar should have one hundred virtues. How many do you possess, my husband?”

Xu Yun said proudly, “All of them.”

His intelligent wife continued, “Character is the most important for all walks of life. My lord, you desire good looks, not good character. How can you claim that you have all the virtues of a scholar?”

Xu Yun was deeply ashamed after hearing his wife’s words. He changed his attitude and henceforth showed the greatest respect toward his wife. He eventually rose through the ranks to become a loyal military general, and raised two sons who also became government officials.